Subject: new Hopf listings From: Mark Hovey Date: 20 Sep 1999 09:48:20 -0400 4 new papers this time. Mark Hovey New papers uploaded to hopf between 8/31/99 and 9/20/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Hovey/sheaves Title: Model category structures on chain complexes of sheaves Author: Mark Hovey Abstract: In this paper, we try to realize the unbounded derived category of an abelian category as the homotopy category of a Quillen model structure on the category of unbounded chain complexes. We construct such a model structure based on injective resolutions for an arbitrary Grothendieck category, as has apparently also been done by Morel. In particular, this works for sheaves on a ringed space, and for quasi-coherent sheaves on a quasi-compact, quasi-separated scheme. However, this injective model structure is not well suited to studying the derived tensor product, so we investigate other model structures. The most successful of these is the flat model structure on complexes of sheaves over a ringed space. This is based on flat resolutions, and is compatible with the tensor product. As a corollary, we get model categories of differential graded algebras of sheaves and differential graded modules over a given differential graded algebra of sheaves. This is the author's first attempt to understand sheaves, so comments from those more experienced with the subject are welcome. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/McAuley/hs Author: Louis F. McAuley Title: A Proof of the Hilbert-Smith Conjecture E-mail: louis@math.binghamton.edu The Hilbert-Smith conjecture is that if G is a locally compact group which acts effectively on a compact connected n-manifold M as a topological transformation group, then G is a Lie group. If G is not a Lie group, then G contains a group isomorphic to a p-adic group A_p which acts effectively on M. It is shown in this paper that A_p can not act effectively on M and, consequently, the Hilbert-Smith Conjecture is true. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Shimomura/beta Title of Paper: On the action of $\beta_1$ in the stable homotopy of spheres at the prime $3$ Author: Katsumi Shimomura Text of Abstruct: The element $\beta_1$ is the generator of the stable homotopy group $\pi_{10}(S^0)$. Here $S^0$ denotes the $3$-localized sphere spectrum. Toda showed that $\beta_1^5\neq 0$ and $\beta_1^6=0$. Here we generalize it to $\beta_1^4\beta_{9t+1}\neq 0$ and $\beta_1^5\beta_{9t+1}= 0$ for $\beta_{9t+1}\in\pi_{144t+10}(S^0)$ with $t\ge 0$. In particular, $\beta_1^4\beta_{10}\neq 0$ and $\beta_1^5\beta_{10}= 0$ for $\beta_{10}$ shown to exist by Oka. This is proved by determining subgroups of $\pi_*(L_2S^0)$, where $L_2$ denotes the Bousfield localization functor with respect to $v_2^{-1}BP$. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Shimomura/L2V-0- Title of Paper: The homotopy groups of the $L_2$-localized mod 3 Moore spectrum Author: Katsumi Shimomura Text of Abstruct: Let $L_2$ denote the Bousfield localization with respect to the 2nd Johnson-Wilson spectrum $E(2)$. The homotopy groups $\pi_*(L_2V(0))$ of the mod 3 Moore spectrum $V(0)$ are determined by using the results on $\pi_*(L_2V(1))$, where $V(1)$ denotes the Toda-Smith spectrum. As an application, we show that $\beta_s\in \pi_*(L_2S^0)$ if and only if s=0,1,2,3,5,6 mod 9. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to Don Davis at dmd1@lehigh.edu with your e-mail address and name. Please make sure he is using the correct e-mail address for you. To see past issues of this mailing list, point your WWW browser to http://www.math.wesleyan.edu/~mhovey/archive/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/algtop.html which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, Purdue seminars, and other math related things on this page as well. The largest archive of math preprints is at http://xxx.lanl.gov There is an algebraic topology section in this archive. The most useful way to browse it or submit papers to it is via the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu To get the announcements of new papers in the algebraic topology section at xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/pub/submissions.html In particular, your abstract is meant to be read by humans, so should be as readable as possible. I reserve the right to edit unreadable abstracts. You should then e-mail Clarence at wilker@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.